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Schreier type theorems for bicrossed products

100%

Agore A., Militaru G.

Open Mathematics

2012

tom 10

nr 2

722-739

We prove that the bicrossed product of two groups is a quotient of the pushout of two semidirect products. A matched pair of groups (H;G; α; β) is deformed using a combinatorial datum (σ; v; r) consisting of an automorphism σ of H, a permutation v of the set G and a transition map r: G → H in order to obtain a new matched pair (H; (G; *); α′, β′) such that there exists a σ-invariant isomorphism of groups H α⋈β G ≅H α′⋈β′ (G, *). Moreover, if we fix the group H and the automorphism σ ∈ Aut H then any σ-invariant isomorphism H α⋈β G ≅ H α′⋈β′ G′ between two arbitrary bicrossed product of groups is obtained in a unique way by the above deformation method. As applications two Schreier type classification theorems for bicrossed products of groups are given.

Weakly-exceptional quotient singularities

81%

Sakovics D.

Open Mathematics

2012

tom 10

nr 3

885-902

A singularity is said to be weakly-exceptional if it has a unique purely log terminal blow-up. In dimension 2, V. Shokurov proved that weakly-exceptional quotient singularities are exactly those of types D n, E 6, E 7, E 8. This paper classifies the weakly-exceptional quotient singularities in dimensions 3 and 4.

Ograniczanie wyników

2 Open Mathematics

1 Agore A.

1 Militaru G.

1 Sakovics D.

2 2012

Wyniki wyszukiwania

Schreier type theorems for bicrossed products

Weakly-exceptional quotient singularities